The paper presents a time-space spectral method for an efficient analysis of rotor–rotor/stator–stator interactions in the framework of the time spectral form harmonic balance method. The method treats time and space harmonics in a coherent way and allows for easy choice of time and passage through the introduction of pseudo-shaft frequency and composite frequency. The proposed method can accommodate passage to passage variation of time-averaged flow field and amplitude of unsteady flow field of a given frequency as needed for rotor–rotor/stator–stator interactions. Minimum change is required to extend an existing harmonic balance flow solver to incorporate the proposed method. The proposed method is the most concise and the simplest one of its kind so far. The first three blade rows of a two-stage fan are used as a test case to demonstrate the validity and effectiveness of the proposed method. Numerical results demonstrate the necessity of including rotor–rotor/stator–stator interaction in an analysis using a frequency-domain method and the capability of the proposed method for such a purpose. It is also concluded from the case study that extra spatial and temporal harmonics are needed to adequately analyze a rotor–rotor/stator–stator interaction.